Squaring Negative Numbers?

Question

Was doing a simple math problem...

Express the number in the form a/b, where a and b are integers.

-2^4 + 3^-1

ooookkk... so heres what i did...

-2^4 + 3^-1 = 16 + 1/3 = 48/3 + 1/3 = 49/3 <-- final answer

However, the answer in the back of the book is not the same.

Book says its -47/3 .. which would be the answer if -2^4 was

-16. I checked the calculator .. said -2^4 is +16 =)

So whats the deal with squaring negative numbers? i thought that squared to an even power it ended up being positive, and squared to an odd power it ends up being negative still.

Am i missing something with there being no parenthesis? someone please please explain it to me =))

Answer 1

I assume if they put it as

-2^4 it means -(2)^4, which will end up as -16

They must put it as (-2)^4 to end up as 16.

Answer 2

you are correct and the book misprinted

Answer 3

Yes, the parenthesis is very important in exponents of negative numbers.

(-1)^4 means (-1)(-1)(-1)(-1) = +1

-1^4 means -(1)(1)(1)(1) = -1

Notice the difference. =]